The Scottish Book (Polish: Księga Szkocka) was a thick notebook used by mathematicians of the Lwow School of Mathematics for jotting down problems meant to be solved. The notebook was named after the "Scottish Café" where it was kept.
Originally, the mathematicians who gathered at the cafe would write down the problems and equations directly on the cafe's marble table tops, but these would be erased at the end of each day, and so the record of the preceding discussions would be lost. The idea for the book was most likely originally suggested by Stefan Banach, or his wife, Łucja, who purchased a large notebook and left it with the proprietor of the cafe.
The Scottish Café (Polish: Kawiarnia Szkocka) was the café in Lwów (now Lviv) where, in the 1930s and 1940s, mathematicians from the Lwów School collaboratively discussed research problems, particularly in functional analysis and topology.
Stanislaw Ulam recounts that the tables of the café had marble tops, so they could write in pencil, directly on the table, during their discussions. To keep the results from being lost, and after becoming annoyed with their writing directly on the table tops, Stefan Banach's wife provided the mathematicians with a large notebook, which was used for writing the problems and answers and eventually became known as the Scottish Book. The book—a collection of solved, unsolved, and even probably unsolvable problems—could be borrowed by any of the guests of the café. Solving any of the problems was rewarded with prizes, with the most difficult and challenging problems having expensive prizes (during the Great Depression and on the eve of World War II), such as a bottle of fine brandy.
For problem 153, which was later recognized as being closely related to Stefan Banach's "basis problem", Stanisław Mazur offered the prize of a live goose. This problem was solved only in 1972 by Per Enflo, who was presented with the live goose in a ceremony that was broadcast throughout Poland.
A total of 193 problems were written down in the book.
Stanisław Mazur contributed a total of 43 problems, 24 of them as a single author and 19 together with Stefan Banach. Banach himself wrote 14, plus another 11 with Stanislaw Ulam and Mazur. Ulam wrote 40 problems and additional 15 ones with others.
Hugo Steinhaus contributed the last one in May 1941 (other sources give March 1941), which involved a question about the likely distribution of matches within a matchbox — a problem motivated by Banach's habit of chain smoking cigarettes — shortly before the German attack on the Soviet Union.
After World War II, Steinhaus at the University of Wrocław revived the tradition of the Scottish book by initiating The New Scottish Book.
The following mathematicians were associated with the Lwów School of Mathematics or contributed to The Scottish Book:
- Stanislaw Ulam
- Karol Borsuk
- Marek Kac
- Stefan Kaczmarz
- Bronisław Knaster
- Kazimierz Kuratowski
- Stanisław Saks
- Juliusz Schauder
- Hugo Steinhaus
- Raikhel, Yuri (January 2010). "Scottish Book: Lviv’s mathematical relic". День. Retrieved November 17, 2011.
- Visser, Jan; Visser, Muriel (2003). "Talking about the unknown by". TechTrends 47 (1): 5–8.
- Mauldin, ed.
- Mauldin, ed.; Kaluza.
- "Stanislaw Mazur". The MacTutor History of Mathematics archive. School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved November 17, 2011.
- Ulam, Stanislaw. The Scottish Book. p. I-II. (sent by Stan Ulam from Los Alamos to Professor Copson in Edinburgh on January 28, 1958)
- Scottish book preface
- Mauldin, R. Daniel, ed. (1981), The Scottish Book, Boston, MA: Birkhäuser Boston, ISBN 978-3-7643-3045-3, MR 666400
- Ulam, Stan, ed. (1958), The Scottish book, English version of Scottish book
- Scottish book
- Scottish book Web page at Home Page of Stefan Banach at University of Gdańsk website
- Manuscript of Scottish book (PDF)
- Typescript of English version of Scottish book (PDF)
- Kawiarnia Szkocka at the MacTutor archive
- Sheldon Axler's review of "The Life of Stefan Banach"
- Kałuża, Roman (1996). Ann Kostant and Wojbor Woyczyński, ed. Through a reporter's eyes: The life of Stefan Banach. Birkhäuser. ISBN 0-8176-3772-9. MR 1392949.
- R. Daniel Mauldin, ed. (1981). The Scottish Book: Mathematics from the Scottish Café (Including selected papers presented at the Scottish Book Conference held at North Texas State University, Denton, Tex., May 1979). Boston, Mass.: Birkhäuser. pp. xiii+268 pp. (2 plates). ISBN 3-7643-3045-7. MR 666400.